They would certainly keep their children form a publicaly and open disputed and discussed form of education.
Why would indoctrination be any easier in a public ond open form of school then in the cellars of some private entities ?
Conservative Americans believe people should have the freedom of choice. We also see PLENTY of socialist indoctrination in our public schools that goes against our moral and family values. Your argument that "because it is in public it cannot happen" falls flat. The schools set up governing bodies called school boards, and between the boards making decisions, the teachers unions wielding power, and individual teachers spreading propaganda in their classrooms, socialist indoctrination is a daily business. I was a public school teacher, and I saw it every single day. That is why 2 million or more American children are now home-schooled and the number is rising all the time.